ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and Fran├žois-Xavier Coudert at CNRS / Chimie ParisTech.
If you use the software in published results (paper, conference, etc.), please cite the corresponding paper (J. Phys. Condens. Matter, 2016, 28, 275201) and give the website URL.

ELATE is open source software. Any queries or comments are welcome at

Summary of the properties

Input: stiffness matrix (coefficients in GPa) of BeAg3 (Materials Project id mp-984719)

       101       99       99        0        0        0  
        99      101       99        0        0        0  
        99       99      101        0        0        0  
         0        0        0       50        0        0  
         0        0        0        0       50        0  
         0        0        0        0        0       50  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 99.667 GPaEV = 82.783 GPaGV = 30.4 GPaνV = 0.36157
ReussKR = 99.667 GPaER = 7.2229 GPaGR = 2.4272 GPaνR = 0.48792
HillKH = 99.667 GPaEH = 46.678 GPaGH = 16.414 GPaνH = 0.42194

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
2 GPa 2 GPa 50 GPa 50 GPa 50 GPa 299 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 2.99 GPa 128.51 GPa 3.3445 TPa–1 3.3445 TPa–1 1 GPa 50 GPa-1.48352.3013Value
Anisotropy 42.98 1.0000 50Anisotropy
Axis 0.0000
0.0000
1.0000
-0.5774
0.5774
-0.5773
0.9983
0.0000
0.0589
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.0000
0.0000
1.0000
-0.6241
0.6241
-0.4701
0.6304
0.6304
-0.4531
Axis
-0.7071
-0.0002
-0.7071
-0.5000
-0.8660
0.0000
-0.7071
-0.7071
0.0000
0.3204
0.3204
0.8915
Second axis

Spatial dependence of Young's modulus



Young's modulus in (xy) plane

Young's modulus in (xz) plane

Young's modulus in (yz) plane

Spatial dependence of linear compressibility



linear compressibility in (xy) plane

linear compressibility in (xz) plane

linear compressibility in (yz) plane

Spatial dependence of shear modulus



Shear modulus in (xy) plane

Shear modulus in (xz) plane

Shear modulus in (yz) plane

Spatial dependence of Poisson's ratio



Poisson's ratio in (xy) plane

Poisson's ratio in (xz) plane

Poisson's ratio in (yz) plane